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When you tap the "find in page" icon, you'll see the same interface that's available when you use the "find in page" feature from the Chrome menu. Use the up/down arrows to see the next/previous match, tap the yellow bars from the scrollbar to go to one of the matches or use the special "find in page" scrollbar.
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Even if you close the find bar, you can easily open it again from Chrome's menu. The nice thing is that Chrome remembers your keywords and the current match.